Mould, carpet - health risk? Also changing bits of carpet?

[NotQuiteCockney]

Ok, we had a water leak problem in a bedroom. The cause has been fixed. The paint and wall look ok, we threw out the bed, but there's blackish mouldy stuff on the carpet (which goes under the bed).

Is the mould a health risk? This is a spare bedroom, but I'd rather not be poisoning our guests. I was planning to change the carpet and vacuum thoroughly underneath.

Can I just cut the carpet off and put down a new piece? I can buy remnants locally, and it's a crappy carpet anyway. And the bit I change will be under the bed. Do I need a special knife? The underlay and the wooden bits with nails sticking up, around the edges, both still look ok.

yeah, ive been told that mould has spores which are bad... cut-out plan sounds good.
bog standard stanley knife should see you right.

Ah, ok, we have a stanley knife.

The mould is dead, now, I think - at least, it's dry, and has stayed dry through a couple of downpours. (The roof guy just shimmied up, did a range of things, charged us £60 and went away. He came highly recommended, but I did want to be sure he'd fixed it!)